No abstract

No abstract

No abstract

A class of univariate fractional ARIMA models with a continuous time parameter is developed for the purpose of modeling long-memory time series. The spectral density of discretely observed data is derived for both point observations (stock variables) and integral observations (flow variables). A frequency domain maximum likelihood method is proposed for estimating the longmemory parameter and is shown to be consistent and asymptotically normally distributed, and some issues associated with the computation of the spectral density are explored.

This paper examines the effects of temporal aggregation on the asymptotic variances of estimators in cointegrated systems+ Two important findings are obtained+ First, estimators based on flow data alone are more efficient than when the data are all stocks or a mixture of stocks and flows+ Second, estimators based on flow data are as efficient as when the data are recorded continuously+ A method of improving efficiency with stock variables is also proposed, and an empirical illustration of the method is provided in the context of long-run money demand regressions+ I thank Roy Bailey, Rex Bergstrom, Roderick McCrorie, a co-editor, and two anonymous referees for helpful com-ments+ I also thank Katsumi Shimotsu for help with some data issues+ None of these individuals are implicated, however, in any possible shortcomings of this paper+ The financial support provided by the ESRC under grant R000221818